The president's bodyguards also have exemptions for some serious automatic weaponry - i.e. military equivalent stuff.
However
There is a distinct attempt to make everything discreet, and you'll note that Airforce One and Marine One may be armoured up and equipped with (one assumes) every ECM system under the sun, but it's not armed with air-to-air weapons - partly because that would make it a valid target.
Instead, it flys with an escort of military fighters - for a "politician" ship I'd assume something similar in most cases; a heavy screened and armoured ship with a whacking huge M-Drive, protected by a formation of Navy or Patrol close escort vessels.
The main ship would be armed, but mostly defensively (lasers, sandcasters) as it's main role is not to fight the enemy, but to keep the guy in stateroom 1 alive whilst it runs like hell for the 100-D limit or for atmosphere.
In the case of someone who's ex-military, or at least has military leanings, and intends to lead from the front, then an ex- or even current-service ship is quite possible - after all, who do you think the local navies answer to?
As to generic others....I'd suggest it's much like law level on a planet - if you're within the patrolled region of a system then their rules apply unless they contradict Imperial law (and sometimes not even then as you get to the raggedy edge of civilization). Defensive armaments (lasers & sandcasters) are probably universally acceptible. Something like a triple particle turret is probably legal outside a few restrictive worlds with very good police fleets, but will raise eyebrows in most civilized places - it's like buying a drum-fed 12-guage rather than a handgun for 'home defence'.
Barbettes probably fall into the same category - they're essentially 'heavy turrets', and their only realistic use is putting holes in someone else's ship. It would probably require a license or a notification of someone that you're packing one, but for a merchant moving regularly through a region where pirate attack is feasible, or if you're a licensed bounty hunter/merc then I suspect no-one would complain.
Bay and (especially) Heavy Bay weapons are unarguably military, I suggest, so unless you've got a very good reason, or are in a region where no-one cares, you'll have dificulty obtaining them. Of course, once you've got a ship armed with them, you are in a position to rather emphatically overrule anyone who wants to object....
Note that one thing that isn't included in the current rules is a heavyweight equivalent to the pop-up turret. There's no reason that a 'slide-out' bay weapon couldn't be created using the same sort of tonnage and cost multipliers: since it's not a standard design it'd cost you a pretty penny, but it would certainly help the...less popular?...nobles maintain their personal security.